Brian Wampler and DIY Stompboxes guys came up with a neat fix a while back. I've implimented it a few times but I think now I've got it even better, where I want it. Where I'm comfortable using it.
I got the idea from here:
The main thing is you don't want this flying board spaghetti monster thing going on. I've had issues with those sorts of things in some of my Boss pedal mods. This simple update puts the parts on a tiny board and connects them physically to the PCB, in place of the original coupling capacitor, using the legs of the new components instead of wires. There is still one wire you need to route from the JFET to the D7 diode on the other side of the board.
The VERIFIED layout is below. You can use a J201 or a 2N5457, whichever is more convenienet.
I tried the "move R1 10K resistor to the input jack" hypothetical mod that was floating around on the DIY forums, but I found it not to solve the problem, so I would recommend skipping that and going straight for this "wampler" mod.
Apparently some of the big mod guys have discovered simpler solution to this problem, but they are not published, so this is the best one available to us DIY people at this time. Also, there's not reason to not use it, it just seems to work.
Also below are pictures of my work and of my "808" Tube Screamer /SD-1. This mod has the pedal fully sorted out so I can use it with confidence from now on. I'm sort of a late comer to the Tube Screamer pedals but they are a lot of fun. It's easy to miss them with so many "spiritual successors" available with extra features, lower prices, or whatever. But this still is the grandaddy of OD, so I'm happy to have a few. I did not like the SD-1 sound at all, so I modded all of mine. My favorite Boss OD is the OD-3. Now that thing, is a serious overdrive. SD-1 are great fun for mods though, and learning how to do this stuff.